Generally most shops deal in these general categories:

Road, sport and mountain

Road: For use on paved roads or bike trails. Generally have a specific trianglular geometry and uses thin, slick road tires. Road bikes range from very compact geometry (racing bikes) to touring bikes (longer wheelbase, more relaxed geometry) and can be made of a number of materials but most often steel, aluminum, carbon and titanium. Prices can be $500 - $15,000!

Sport: general category bikes. Includes hybrids. Can be used on road or on easy trail/fire roads. Not really for serious riding or long distances (OK I realize people do use them for serious riding - it's just not the best choice). If your plan is to do rides under 20 miles around a bike path or on a rail trail, this type of bike will work for you.

mountain: mountain bikes have its share of hybrids (this is really a huge wide category) as well but generally mountain bikes are:

rigid - no suspension - the favorite of those that enjoy singlespeeds (no gearing. There are road singlespeeds and "fixies" as well) and hard core riding.

hard tail - front suspension only. Very adequate on most trails, singletrack and even hard core stuff although not great for downhill (see below). HT's are lighter than full suspension bikes which means they climb well and are generally less expensive than fullies but not always.

full-suspension - has a front suspension fork and rear shock. Fullies can take alot of jiggle out of the trail and can be used on most trails, singletrack, fireroads etc. Can be "cross-country" or "all-mountain".

downhill rigs: Large heavy bikes with huge front forks and long travel shocks. Push them up hill and ride them down steep stuff.

Also included in the mountain category are cyclo-cross bikes - bikes made specially for trail and paved road.

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Anyway its hard to really discuss all the types of bikes so easily. But I always tell people this - decide what you want to do. Do you want to ride road or ride trail and buy the best bike for the money that is built for what you want to do. Yes I realize hybrid bikes are cheaper and can do both, but plan on upgrading in the future to either a road or mountain bike if you stay with and want to grow in the sport.